The main fundamental mathematical tools to be developed in this endeavour are a discrete analogue to the theory of regularity structures, as well as a number of nonlinear

invariance principles.

Merely demonstrating that Einstein's master equation of general relativity satisfies his equivalence and invariance principles takes reams of paper.

Another was the extension of the invariance principle to accelerating observers: the laws of nature themselves should be identical for all observers, regardless of the magnitude or direction of their acceleration.

Invariance principles are the golden eggs of economics.

Thus, the invariance principle holds in Regime D because revenue sharing has no effect on the distribution of talent and thus does not affect pre-shared club revenues.

They cover random systems with covariance inequalities, moment and maximal inequalities, the central limit theorem, the "almost sure" convergence,

invariance principles, the law of the iterated logarithm, statistical applications, and integral functionals.

Dilworth does go on to point out that the principles do exist in explicit, refined forms, such as spatial and temporal

invariance principles, conservation laws, and the law of inertia.

Similarly, conservation laws and symmetry laws are now grouped under various laws of invariance: "In fact, if the universal law of nature should be discovered, invariance principles would become merely mathematical transformations which leave the law invariant.

Wigner, "The Role of Invariance Principles in Natural Philosophy," in Symmetries and Reflections: Scientific Essays of Eugene P.

Thus, people may be more rational than the psychological literature gives them credit for, and applications of the SEU model may be susceptible to some violations of

invariance principles.

Invariance principles are one or more clauses establishing constant of motion in a general sense.

These clauses are written as conservation principles for the dynamic behavior and as invariance principles for the structure.